An experimental side without the likes of Lionel Messi, Sergio Aguero or Gonzalo Higuain gave a commanding display in the first game of a four-team tournament that also features Brazil and Saudi Arabia.
Martinez, who has scored one goal in four Serie A appearances for Inter this season, provided a reminder of his abilities by opening his account for his country after earning his first start.
In-form Juventus forward Paulo Dybala led the Argentina attack admirably, and the 24-year-old provided an assist for Roberto Pereyra to score the second as the Watford striker made his first international appearance for three years.
Fiorentina centre-back German Pezzella added a third in the closing stages before Franco Cervi made it 4-0 in injury time to send Argentina into its game against Brazil on a high.
Argentina took control early on and when Marcos Acuna crossed from the left after 18 minutes, Martinez nipped in ahead of his marker to apply a clinical near-post header, sending the ball high into the net.
Less than 10 minutes after coming on as a substitute, Pereyra received a short pass from Dybala inside the Iraq penalty area and had time to take aim before hooking the ball into the corner of the net.
Dybala almost got the reward his performance deserved when substitute Giovanni Simeone teed him up for a curling shot that drew a one-handed diving save from Jalal Hassan.
Eduardo Salvio's flick-on from a corner found Pezzella at the far post in the 82nd minute and the defender made amends for his earlier miss, heading the ball high into the net to make it 3-0.
Benfica winger Cervi added Argentina's fourth and his first for his country when his jinking 30-yard run showed shades of Messi before he slammed a left-footed finish into the far corner of the net with practically the last kick of the game.